You are mistaken.

The DSA signature scheme is assumed to be a EUF-CMA or sEUF-CMA hard problem. However, after decades there has been no formal proof to be reducable to the DL-assumption (or Computational Diffie Hellman assumption or Decisional Diffie Hellman assumption). We also think that the mathematical problems on an elliptic curve and under Zp* are equivalent.

This is in stark contrast to the Schnorr Signature Sheme where there is a formal proof in the random oracle model under DL assumption to be EUF-CMA.

Any news about findings about DSA in Zp* or elliptic curve are worrisome. We basically wish that there shouldn't even be something to talk about. Especially any hints that there is a connection between signature, nonce and private key. Which is what this paper hints at.

To people that aren't familiar with cryptography: This might sound chinese to you. But what we're talking about here realistically is that in a few decades somebody finds out that the signature scheme is reducable to DL, DH or DDH - which would be huge news in cryptography but would still mean that nobody can forge signatures without breaking DL, DH or DDH - which they can't. Also, if somebody was to find a connection between signature, nonce and private key - that doesn't mean its exploitable by PPT algorthms - which wouldn't be surprising due to DSAs structure.